To get your rims back to their original state, unfortunately the only way would be to have them refinished, or if you want to do it yourself you can try using a metal polish. Wheel/Rim Cleaners aren't really made for removing oxidation.

Unfortunately at this time we do not offer any polishing compounds for anything. We may release something for paint in the future and a slight chance of a metal polish for what you are looking for.

But, I would recommend getting this product -- https://www.amazon.com/Simichrome-390050-Metal-Polish-Tube/dp/B0002YUQ4E

We have no affiliation with this company, but I've used it. It's cheap and it works great for polishing all types of metals, including chrome.

And if you don't want to hand polish your wheels, get something called a polishing cone. You just stick it on your drill, add some polish and buff your wheels. Something like this -- https://www.amazon.com/Mothers-05146-PowerCone-Metal-Polishing/dp/B001MXTOKQ